Advanced Structural Analysis.ppt tr12564

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1. MODERN INSTITUTE OF ENGINEERING & TECHNOLOGY NAME : ABHISEK DEB ROLL NO : 26901322025 BRANCH : CIVIL ENGINEERING SUBJECT : ADVANCED STRUCTURAL ANALYSIS{CE(PE) 7 04B } SEMESTER : 7TH YEAR : 2023-2024

2. MATRIX METHOD OF STRUCTURAL ANALYSIS & FINITE DIFFERENCE AND RELAXATION TECHNIQUE

3. CONTENT INTRODUCTION WHAT IS MATRIX METHOD FLEXIBILITY MATRIX METHOD DISPLACEMENT OR STIFFNESS MATRIX METHOD FINITE ELEMENT METHOD (FEM) FINITE ELEMENT ANALYSIS (FEA) APPLICATIONS OF FEM AND FEA

4. INTRODUCTION Based on the type of unknowns used in the matrix, it can be classified as the flexibility and stiffness matrix methods. These methods of analysis of indeterminate structures will be discussed in this article. Matrix methods for analyzing indeterminate structures are based on the principle of matrix algebra, And they can also be implemented in terms of computer programing. Due to its advantages, many software applications use the matrix method to analyse indeterminate structures.

5. WHAT IS MATRIX METHOD The Matrix Method is one of the two methods for analysing the indeterminate structure, depending on the unknown chosen for analysis. If the unknown is taken as forces, it is known as the force method (Flexibility method), and if the unknown is taken as displacements, it is known as the displacement method (Stiffness method). The matrix method of analysis of indeterminate structures provides a tool for solving the differential equations used in the analysis. In the matrix method, unknowns are written in terms of the matrix element, and it can be solved using the concept of matrix algebra

6. FLEXIBILITY MATRIX METHOD The flexibility matrix method is also a method of analysis of indeterminate structures. This method comes under the force method of analysis. In this method, forces are taken as unknown, and equations are expressed in terms of these forces. An additional compatibility condition equation is developed to find all the unknown forces. This method is suitable when the static indeterminacy is less than kinematic indeterminacy.

7. DISPLACEMENT OR STIFFNESS MATRIX METHOD The stiffness matrix method comes under the displacement method of analysis of indeterminate structures. In this method, displacements at the joints are taken as unknowns, and equations are expressed in terms of these unknown displacements. Additional joint equilibrium equations are developed to find the unknown displacement. This method is suitable when the Kinematic indeterminacy is less than the static indeterminacy.

8. FINITE ELEMENT METHOD (FEM) Developed by engineers in the mid-1950s, FEM provides a numerical solution for a complex problem, which allows for some level of error. Usually, it’s used when a math equation is too complex to be solved in a typical fashion. A simple way to understand FEM is to look at it as separating a large problem into a series of smaller ones (“finite elements”). This makes the overall problem easier to investigate. Engineers use FEM when they need to develop an adoptable design that’s practical but not necessarily perfect for a particular application.

9. FINITE ELEMENT ANALYSIS (FEA) The mathematical equations behind FEM are applied to create a simulation, or what’s known as a finite element analysis (FEA). This simulation is used to provide a structural analysis of how a particular product or design would react under stress in the real world. The simulation breaks down the entire model into smaller elements within a mesh, which engineers use to test how the different elements of a design interact and perform under simulated stressors.

10. APPLICATIONS OF FEM AND FEA Traditionally, FEM was used to test designs within aerospace and civil engineering, but it is now expanding to other disciplines, including biomechanics, thermomechanical, fluid-structure interaction, biomedical engineering, ferroelectric, thermo-chemo-mechanical problems, piezoelectric, and electromagnetics. The mathematical principles behind FEM can also be applied to other areas, like computational fluid dynamics (CFD) as well as the thermal dynamics of a structure